Abstract: Many image reconstruction tasks amount to solve ill-posed inverse problems. Indeed, measurement devices typically cannot record all the information needed to recover the sought-after object; furthermore, the operators that model these devices are seldom accurate and data are corrupted by various perturbations. A common approach to find an approximate to the unknown object is regularization. The key points are the correct choices of the data fidelity term and the regularization term, as well as the trade-off between these terms. This is a challenging problem since the optimal solutions of the whole functional should correctly reflect the knowledge on the data-production process and the priors on the unknown object. The optimal solutions usually cannot be computed explicitly and iterative schemes are used.
This symposium focus on imaging inverse problemsí» mathematical models, numerical algorithms, theoretical analysis and various applications, especially, applied to CT reconstruction and some processing techniques for images.

MS-Th-D-46-113:30--14:00 A PDE-free variational model for multiphase image segmentationJulia, Dobrosotskaya (Case Western Reserve Univ.)Guo, Weihong (Case Western Reserve Univ.)Abstract: We introduce a PDE-free variational model for multiphase image segmentation in a modified diffuse interface context. This model uses such features of diffuse interface behavior as coarsening and phase separation to merge relevant image elements (coarsening) and separate others into distinct classes (phase separation). The model has edge-preserving feature that naturally balances out the regularity implemented by wavelet Ginzburg-Landau energy. Numerical experiments show that the model is robust to noise yet can segment fine details.

MS-Th-D-46-214:00--14:30CT metal artifacts reduction by an iterative algorithm based on inpaintingLee, Chang-Ock (KAIST)Jeon, Soomin (KAIST)Abstract: The streaking artifacts in computed tomography (CT) image caused by the metallic objects (dental implants, surgical clips, or steel-hip) limit the applications of CT image. We propose a new algorithm for reducing the streaking artifacts in CT images. We inpaint the corrupted part in sinogram, iteratively, using the basic principle of CT. The numerical experiments show that our algorithm reduces the metal artifacts efficiently. We analyze the simulation results both quantitatively and qualitatively.

MS-Th-D-46-415:00--15:30Limitations of splitting methods for total variation-based
image reconstructionHintermueller, Michael (Humboldt-Univ. of Berlin)Abstract: Variable splitting schemes for image
reconstruction problem with total variation regularization (TV-problem) in
its primal and pre-dual formulations are considered. For primal splitting
it is shown that quasi-minimizers of the penalized problem are asymptotically related to the solution of the original TV-problem. For the predual
formulation, a family of parametrized problems is introduced and a
parameter dependent contraction of an associated fixed point iteration is
established.